Area of triangles with a part of a circle removed

You can start by computing the area of region which is shaded in the attached picture. This region is a difference between an arc and a triangle.

However, I don't see what exactly I should consider given in your picture. Some numbers simply don't work together. (If the large circle has radius 12cm and the small has radius 5cm, I do not think it is possible to have 7 cm where you wrote it between the circles. Also if 3 cm is where you wrote, this would mean 5^2+8^2=12^2. I think I'm getting something wrong - could you clarify the question?)